# Properties

 Label 3630.23 Modulus $3630$ Conductor $1815$ Order $44$ Real no Primitive no Minimal yes Parity even

# Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter

sage: H = DirichletGroup(3630)

sage: M = H._module

sage: chi = DirichletCharacter(H, M([22,33,28]))

pari: [g,chi] = znchar(Mod(23,3630))

## Basic properties

 Modulus: $$3630$$ Conductor: $$1815$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$44$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{1815}(23,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 3630.bi

sage: chi.galois_orbit()

pari: order = charorder(g,chi)

pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

## Values on generators

$$(1211,727,3511)$$ → $$(-1,-i,e\left(\frac{7}{11}\right))$$

## Values

 $$-1$$ $$1$$ $$7$$ $$13$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$ $$1$$ $$1$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{7}{44}\right)$$
 value at e.g. 2

## Related number fields

 Field of values: $$\Q(\zeta_{44})$$ Fixed field: Number field defined by a degree 44 polynomial